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Balancing
a
Two-Wheeled
Segway
Robot
by
Maia
R.
Bageant
Submitted to the
Department
of
Mechanical
Engineering
in
partial
fulfillment
of
the
requirements
for
the
degree
ofEiMASSACHUSETTS
NSTITUTE
OF
TECHN!-tros
y
Bachelor
of
Science
in
Mechanical
Engineering
OCT
2
0
2011
at
the
-T
U A i
MASSACHUSETTS
INSTITUTE
OF
TECHNOLOGY
ARCHNES
June
2011
©
Massachusetts
Institute
of
Technology
2011.
All
rights
reserved.
Author
.
.......
Department
of
Mechanical
Engineering
May
6,
2011
7-v
/
Certified
by.............................................
Harry
Asada
Ford
Professor
of
Engineering
Thesis
Supervisor
Accepted
by..
Samuel
C.
Collins
Profei
Undergraduate
Officer
Balancing
a
Two-Wheeled
Segway
Robot
by
Maia
R.
Bageant
Submitted
to
the
Department
of
Mechanical
Engineering
on
May
6,
2011,
in
partial
fulfillment
of
the
requirements
for
the
degree
of
Bachelor
of Science
in
Mechanical
Engineering
Abstract
In
this
thesis,
I
designed
and
constructed
hardware
for
a
two-wheeled
balancing
Seg-
way
robot.
Because
the robot
could
not
be
balanced based
on a
control
system
derived
from
the
original
analytical
model,
additional
system
dynamics
in
the
form
of
frictional
losses in
the
motors
were
incorporated.
A
SISO
PID
compensator
and
a
SISO
lead-lag compensator
were
designed
to
balance
the robot
based
on
the
new
model;
both
showed
acceptable
system responses
but
were
subject
to
high-frequency
oscillation.
A
SISO
state
feedback
controller
was
also
designed,
and it
was
successful
in
creating
stability
in
simulation
and removing
the
high-frequency
oscillation
effects.
The
robot
was
rebuilt
using
new
parts
that
better
represented
its
ideal
model,
and
software
was
created
using
National
Instruments
LabVIEW
to
control
the
robot.
Thesis
Supervisor:
Harry
Asada
Title: Ford
Professor
of
Engineering
Acknowledgments
The
author
would
like
to
acknowledge
her
advisor,
Professor
Asada,
for
conceiving
of
the
project
and
providing
guidance
during
its
execution;
James
Torres,
for
being
readily
available
to
procure
hardware
and
answer
questions
of
any
sort;
and
her
family,
for
supporting
her
through
even
the
toughest
of
times.
Contents
1
Motivation
13
2
Introduction
and
Background
15
2.1
The
Inverted
Pendulum
and
Two-Wheeled
Robots
...........
15
2.2
Physical
Model
of
the
Robot
......
.......................
16
2.3
PID
Control
. .
.
. .
. .
. .
.
. .
. .
. .
. .
.
. .
. .
. .
.
. .
. .
. .
18
3
Modified
Model
21
3.1
Description
of
Modifications
.
. .
. .
.
. .
.
. .
.
. .
.
. .
.
. .
. .
.
21
3.2
Modified
Physical
Model
of
the
Robot
. .
. .
.
. .
. .
.
. .
. .
.
. .
22
3.3
Modified
System
Response
.
.
. .
. .
.
. .
. .
.
. .
. .
.
. .
. .
.
. .
23
4
Achieving
Stability
by
Root
Locus
Shaping
27
4.1
W
hy
Root
Locus?
. .
.
. .
.
. .
.
. .
.
. .
.
.
. .
.
. .
.
. .
.
. .
.
.
27
4.2
Necessity
of
the
Integrator
. .
.
.
. .
.
.
. .
.
. .
.
.
. .
.
.
. .
.
. .
28
4.3
Lead-Lag
Compensator
Design
. .
.
. .
. .
.
. .
. .
.
. .
. .
.
. .
. .
30
4.4
PID
Compensator
Design
.
.
. .
. .
.
. .
. .
.
. .
. .
.
. .
. .
.
. .
32
5
Achieving
Stability
by
Pole
Placement
37
5.1
Derivation
of
the
State
Space
Model
.
. .
. .
.
. .
.
. .
.
. .
.
. .
.
37
5.2
Pole
Placem
ent
. .
. .
.
. .
. .
.
. .
. .
.
. .
. .
.
. .
. .
.
. .
. .
.
38
5.3
System
Performance
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
.
. .
40
6
Hardware
Design
43
6.1
B
ody
. . .
. . .
. . .
. . .
. .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
.
43
6.2
D
rive
System
. .
. . .
. . .
. . .
. . . .
. . .
. . .
. .
. . .
. . .
. .
43
6.3
Sensors........
............
............
. .......
..
44
6.3.1
Inertial
Measurement
Unit
. .
. . .
. . .
. .
. . .
. . .
. .
. .
44
6.3.2
Encoders
. .
. .
. . .
. .
. . .
. . .
. .
. . .
. .
. . .
. .
. . .
47
6.4
Processing
Unit
. .
. .
. . .
. .
. . .
. . .
. .
. . .
. .
. . .
. .
. . .
47
7
Software
Design
49
8
Conclusion
51
8.1
C
onclusion
. . .
. . .
. .
. . .
. . .
. .
. . .
. . .
. .
. . .
. . .
. .
. 51
8.2
Further
Study
. .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. .
52
A
Numerical
Constants
53
B
Calculation
of
Frictional
Losses
55
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